Question

The internal energy of a gas is given by U = 1.5 pV. It expands from 100 cm3 to 200 cm3 against a constant pressure of 1.0 × 105 Pa. Calculate the heat absorbed by the gas in the process.

Answer 1

The heat absorbed by the gas is 25 J

Explanation:

Given data:

Internal energy U = 1.5 pV

Pressure = 1 × 10^5 Pa

Change in volume "dV" = (200 – 100) cm^3 = 100 cm^3 = 10^–4 m^3

dU = 1.5 × 10^5 × 10^–4 = 15

dW = 1.5 x 10^5 x 10^-4 = 15

dW = 10^5 x 10^-4 = 10

Heat absorbed y the gas:

dQ = dU + dW = 10 + 15 = 25 J

Thus the heat absorbed by the gas is 25 J.

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Answer 2

The heat absorbed by the gas in the process is 25 J.

Explanation:

Step 1:

Let ∆V is considered as the change in volume of the gas.

$\begin{aligned}\Delta V &=(200-100) \mathrm{cm}^{3}=100 \mathrm{cm}^{3} \\&=10^{-4} \mathrm{m}^{3}\end{aligned}$

$p=1 \times 10^{5} \mathrm{Pa}$

∆U = 1.5 pV

∆U   is Change in internal energy of the system,

$\Delta U=1.5 \times 10^{5} \times 10^{-4}=15 \mathrm{J}$

∆W = p∆V

$=10^{5} \times 10^{-4}=10 \mathrm{J}$

Step 2:

Using the thermodynamics first law , we get

∆Q = ∆U + ∆W = 10 + 15 = 25 J

So, the heat that the device absorbs is 25 J.