Assignments Ice, Water, Steam Competency Quiz Internal Energy, Heat & Work Problem Set

Calorimetry and Energy Cycles Edward A. Mottel Department of Chemistry Rose-Hulman Institute of Technology

Topics  Reading assignment: Chang: Chapter , 11.8  This lecture describes calorimetric methods to measure heat flow. an application of the conservation of energy by using energy cycles to solve a thermodynamic problem. the calculation of work performed by an expanding gas for various pathways.

Calorimeter q system + q surroundings = 0 GOAL: limit heat gain of surroundings to zero An insulated device in which reactants are mixed together, and the change in temperature of the products and the calorimeter is used to calculate the heat of reaction.

Constant Pressure Calorimeter Adiabatic calorimeter q = 0 No heat flow between system and surroundings System: reactants and part of calorimeter touching the reactants Surroundings: everything else q Vacuum or insulated space Thermometer

Energy Balance q system + q surroundings = 0 q solution + q calorimeter = 0 0

Constant Pressure Calorimeter Any heat released is trapped by the solution and calorimeter unit. No heat is transferred to the surroundings. The heat flow in this process is equal to which thermodynamic term, q p or q v ? = 0+ (m solution. C p,solution ·  T)(C calorimeter ·  T) q solution + q calorimeter = 0

Constant Pressure Calorimeter Example  A steel bolt (17.93 g) is heated in a Bunsen burner flame for four minutes. The bolt is placed in 209 mL of water at 19.1 °C. The temperature of the water rises to 26.0 °C. The heat capacity at constant pressure for iron is J·g –1 · K –1. What is the temperature of the hot bolt?

Constant Volume Calorimeter  Oxygen Bomb Calorimeter A thick walled device in which a reactant is combusted in air or oxygen. Heat flows from the device to its immediate surroundings, and the temperature change of these surroundings is used to determine the heat of reaction.

Oxygen Bomb Calorimeter Thermometer water Ignition source

Constant Volume Calorimeter  Oxygen Bomb Calorimeter The water surrounding the reaction container behaves as a large heat sink. ·The bomb and immediate surroundings are responsible for the calorimeter constant, also called the "water equivalent". q = m · C p ·  T ·m is the water equivalent of the calorimeter ·C p is the heat capacity of water

Constant Volume Calorimeter  Often the surroundings are at constant pressure, even though the reaction is performed at constant volume. Because pressure may be building up, it is advantageous to keep  T small.

Constant Volume Calorimeter Example  2.40 grams of methane (MW =16.0) is burned in a bomb calorimeter with a water equivalent of grams.  The initial temperature of the calorimeter was 22.3 °C, the final temperature was 25.9 °C.  Assume the heat capacity of water is J·g –1 ·K –1.  Calculate the heat evolved per mole of CH 4. The heat flow in this process is equal to which thermodynamic term,  H or  E?

6/30/2015 Energy Cycles  Reading Assignment: Chang, Chapter 6.6  This lecture involves the concept of thermodynamic energy cycles and calculation of the heat energy released by these cyclic processes.  The importance of different pathways is exemplified by the Carnot cycle and Hess' Law.

6/30/2015 Energy Cycles  A series of energy steps following a defined pathway in which the final step returns the system to the original state conditions.  Pathways Isobaric Isothermal (constant external pressure) Isothermal (varying external pressure) Adiabatic

6/30/2015 Sublimation of Water at 0  C sublimation H 2 O (s, 0  C)H 2 O (g, 0  C) H 2 O (g, 100  C) H 2 O ( l, 100  C) H 2 O ( l, 0  C) Which thermodynamic terms are associated with each step? heat capacity of steam enthalpy of vaporization heat capacity of liquid water enthalpy of fusion

6/30/2015 Determine the Enthalpy of Sublimation of Water at 0  C Assume the heat capacity of water vapor is constant from 0 °C to 200 °C. H 2 O (s, 0  C)H 2 O (g, 0  C) H 2 O ( l, 100  C) H 2 O ( l, 0  C)H 2 O (g, 100  C) sublimation +50 cal/g +209 J/g -540 cal/g j/g -100 cal/g -418 J/g -80 cal/g -335 J/g +670 cal/g J/g ?

6/30/2015 Ice, Water, Steam Competency Quiz  Select various masses of ice, water and steam at temperatures consistent with the phases.  Determine the final temperature of the mixture and the number of grams of each phase present in the final mixture.  Confirm your answer with the program ICEWATER in the class folder.

6/30/2015 Isothermal Expansion Constant External Pressure  1.5 atm One liter of a compressed gas in a cylinder causes a piston to expand against a constant external pressure of 1.5 atm until the total volume of the gas in the cylinder is three liters. The initial and final temperature of the gas in the cylinder is the same. Sketch a graph of this process

6/30/2015 Isothermal Expansion Constant External Pressure Volume (L) P ext (atm)

6/30/2015 Isothermal Expansion Constant External Pressure Volume (L) P ext (atm) Work may be represented as the area under the curve. work = -   VfVf ViVi P dV= - P   VfVf ViVi dV = - P (V f - V i )

6/30/2015 Energy Units  L  atm can be converted to more common energy units (e.g., J or cal) by using the value of R as a conversion factor. Determine the work done in calories and joules work = - (1.5 atm) (3.0 L L) = -3.0 L  atm

6/30/2015 Energy Units Determine the work done in calories and joules work = - (1.5 atm) (3.0 L L) = -3.0 L  atm = -3.0 L  atm × cal  mol -1  K L  atm  mol -1  K -1 = -73 cal = -3.0 L  atm × J  mol -1  K L  atm  mol -1  K -1 = -304 J

6/30/2015 Isobaric Work Ideal Gas H 2 O(g, 100 °C) H 2 O(ℓ, 100 °C) H 2 O(g, 200 °C) work = -   VfVf ViVi P dV= - P ΔV work = - P ΔV =- Δ(nRT) work = - nR ΔT work = - Δn RTwork = - Δn gas RT

6/30/2015 Engines  An engine is a machine which can perform work.  The expansion of a gas in a piston can do work.  Describe the activities of an expanding gas at constant external pressure.

6/30/2015 Engines Constant External Pressure  1.5 atm Expansion Stroke  1.5 atm Compression Stroke  1.5 atm An engine is a machine which can perform work. work being done BY gaswork being done ON gas

6/30/2015 Engines Volume (L) P ext (atm) expansion cycle As described this does not represent a practical engine because the final state does not equal the initial state. compression cycle How much work is done in this overall process?

6/30/2015 Isothermal Expansion Decreasing External Pressure  4.5 atm One liter of a compressed gas in a cylinder causes a piston to expand against a decreasing external pressure until the total volume of the gas in the cylinder is three liters.  2.25 atm  1.5 atm The initial and final temperature of the gas in the cylinder is the same. Sketch a graph of this process

6/30/ Volume (L) P ext (atm) 3 4 Isothermal Expansion Decreasing External Pressure

6/30/2015 Isothermal Expansion Decreasing External Pressure PV = nRT Work may be represented as the area under the curve. work = -   VfVf ViVi P dV Volume (L) P ext (atm) 3 4 The pressure term is rewritten in terms of volume. = -   VfVf ViVi dV nRT V = - nRT ln VfVf ViVi     Isothermal Expansion Decreasing External Pressure

6/30/ Volume (L) P ext (atm) 3 4 Isothermal Expansion Decreasing External Pressure Is there any net heat flow in this process?  E = q + w the internal energy of a phase is a function of its temperature  E = q v = m  C v  T isothermal = 0 Is heat flowing into or out of the system?

6/30/ Volume (L) P ext (atm) 3 4 Isothermal Expansion Decreasing External Pressure The decreasing external pressure piston performs more work (greater efficiency) than a piston working against a constant external pressure equal to P final. Constant External Pressure

6/30/ Volume (L) P ext (atm) 3 4 Isothermal Expansion Decreasing External Pressure If the process is reversed, how much work is done? If the isothermal expansion process is reversed by isobaric compression, how much work is done?

6/30/2015 Gas Expansion Room temperature gas colder gas When a gas expands against a low restraining pressure why does it cool?  E = q + w adiabatic expansion q = 0

6/30/2015 Gas Expansion Carbon Dioxide Fire Extinguisher Why is it dangerous to point a carbon dioxide fire extinguisher at a person? liquid CO 2 gaseous CO 2

6/30/2015 Adiabatic Expansion  The same process occurs, except there is no heat flow allowed between the system and the surroundings.  On expansion, the gas will cool and follows a non-isothermal PV curve. PV  = constant for an ideal diatomic gas,  =1.67

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Adiabatic Expansion  In each of the examples, a different pressure change pathway is followed by the gas.  How much work will be done if the process is reversed to complete the cycle?

6/30/2015 Carnot Cycle  Consists of two isothermal and two adiabatic steps, occurring alternatively.  One of each type of step is involved in compression and expansion.

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