Day 5 - Various Heat Cycles & ActivPhysics

Heat engine via simple gas cycle:

By following the lab manual instructions our group calculated the change in internal energy, work, and heat transferred during each transition of the cycle. We used the formula E=3/2nRT and subsituted PV for nRT, which allowed us to to use the new formula to calculate the energy at each point. The difference between two points was calculated to find the internal energy's change. The formula W=P(delta V) was used to calculated work for each step. Our group used Q=(delta E)+ W to find Q. In between the points 4 and 1 and 2 and 3 no work was done since the volume was constant. Due to this we know that (delta E) is equal to Q.

ActivPhysics Section 8.7 : Heat Capacity

Question 6: Heat and Temperature Change Numbers
RESET the simulation. RUN the simulation and STOP it when the system temperature is about 400K. Record the heat transfer that has already occurred and the present temperature. Then RUN the simulation again and quickly stop it. Record the heat transfer DQ and temperature again. Repeat the process several times. Use the numbers you have obtained to estimate the constant pressure molar specific heat capacity of this ideal gas. When you are finished, compare your answer to that of the Advisor.

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Question 7: A More Accurate Heat Capacity Measurement
RESET the simulation to bring the temperature to 200K. Note the numbers on the meter. Press RUN and then stop the simulation when the temperature reaches about 800K and note the numbers in the meter. Make an accurate calculation of the constant pressure molar heat capacity of the ideal gas. When you are finished, compare your answer to that of the Advisor.

Question 8: A Theoretical Determination of the Constant-Pressure Molar Heat Capacity of an Ideal Gas

	Apply in symbols the first law of thermodynamics to this process--warming the gas at constant pressure.
	Substitute the expression for the internal thermal energy change of the gas in terms of the temperature change (use only symbols--not numbers).
	Substitute an expression for the work done by the gas in terms of the pressure, the initial volume and the final volume of the gas (use only symbols--not numbers).
	Then use the ideal gas law to rewrite this expression for work in terms of initial and final temperatures and other quantities (symbols only--not numbers).
	Rearrange this last equation so that the left side equals the molar heat capacity at constant pressure. You should have only constants remaining on the right side of the equation. Calculate the value of these constants and compare to your answer in Question 7. Hopefully, the values are the same!

If you have trouble, you can get help from the Advisor.

Carnot Cycle:

Derivation of Molar heat capacity at constant Pressure: