Question

A monatomic ideal gas has pressure p1 and temperature T1. It is contained in a cylinder of volume V1 with a movable piston, so that it can do work on the outside world.Consider the following three-step transformation of the gas:

a)The gas is heated at constant volume until the pressure reaches Ap1(where A>1).
b)The gas is then expanded at constant temperature until the pressure returns to p1.
c)The gas is then cooled at constant pressure until the volume has returned to V1.
d)It may be helpful to sketch this process on the pVplane.
How much heat Q1 is added to the gas during step 1 of the process?Express the heat added in terms of p1, V1, and A.

Answer 1

In step 1 of the process, the heat added to the gas can be calculated using the formula Q1 = (3/2)nRV∆T. In terms of p1, V1, and A, Q1 = (3/2)nR(V1/A - V1).

Step-by-step explanation:

In step 1 of the process, the gas is heated at constant volume. During this step, the heat added to the gas can be calculated using the formula:

Q1 = ncV∆T

Where Q1 is the heat added, n is the number of moles of gas, cV is the molar specific heat at constant volume, and ∆T is the change in temperature.

Since the gas is monatomic, the molar specific heat at constant volume for an ideal gas is given by:

cV = (3/2)R

Where R is the gas constant.

Thus, the heat added can be expressed as:

Q1 = (3/2)nRV∆T

In terms of p1, V1, and A:

Q1 = (3/2)nR(V1/A - V1)