A piston contains 0.232 mol of a
diatomic gas. The piston is compressed
while 57.5 J of heat are removed.
The temperature changes by .
How much work is done by the gas?

Ask by Todd Warren. in the United States

Mar 27,2025

Question

A piston contains 0.232 mol of a
diatomic gas. The piston is compressed
while 57.5 J of heat are removed.
The temperature changes by .
How much work is done by the gas?

Ask by Todd Warren. in the United States

Mar 27,2025

UpStudy AI · Accepted Answer

We start with the first law of thermodynamics

$$
\Delta U = Q - W,
$$

where

• $$Q$$ is the heat added to the gas (if heat is removed, $$Q$$ is negative),  
• $$W$$ is the work done by the gas, and  
• $$\Delta U$$ is the change in internal energy.

Because $$57.5\,\text{J}$$ of heat are removed,

$$
Q = -57.5\,\text{J}.
$$

For an ideal gas, the change in internal energy is

$$
\Delta U = n\,C_V\,\Delta T,
$$

where  
• $$n = 0.232\,\text{mol}$$ is the amount of gas,  
• $$\Delta T = 68.0\,\text{K}$$ (a change in Celsius is the same numerical change in Kelvin), and  
• $$C_V$$ is the molar heat capacity at constant volume.

For a diatomic gas (at room temperature, where vibrational modes are not excited) the molar heat capacity at constant volume is

$$
C_V = \frac{5}{2}R,
$$

with

$$
R = 8.314\,\text{J/mol}\cdot\text{K}.
$$

Thus,

$$
C_V = \frac{5}{2}(8.314) \approx 20.785\,\text{J/mol}\cdot\text{K}.
$$

Now we calculate the change in internal energy:

$$
\Delta U = 0.232 \times 20.785 \times 68.0.
$$

First, calculate the product

$$
20.785 \times 68.0 \approx 1413.38\,\text{J/mol},
$$

then

$$
\Delta U \approx 0.232 \times 1413.38 \approx 327.91\,\text{J}.
$$

Using the first law, solving for $$W$$:

$$
W = Q - \Delta U.
$$

Substitute the known values:

$$
W = -57.5\,\text{J} - 327.91\,\text{J} \approx -385.41\,\text{J}.
$$

Thus, the work done by the gas is

$$
W \approx -3.85 \times 10^2\,\text{J}.
$$

The negative sign indicates that work is done on the gas (the gas is compressed).
The work done by the gas is approximately $$-385.41\,\text{J}$$.

A piston contains 0.232 mol of a
diatomic gas. The piston is compressed
while 57.5 J of heat are removed.
The temperature changes by .
How much work is done by the gas?

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A piston contains 0.232 mol of a diatomic gas. The piston is compressed while 57.5 J of heat are removed. The temperature changes by . How much work is done by the gas?

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A piston contains 0.232 mol of a
diatomic gas. The piston is compressed
while 57.5 J of heat are removed.
The temperature changes by .
How much work is done by the gas?