Ncert Exercises & Solutions

An ideal gas undergoes an isothermal process from some initial state i to
the final state $f$ .

(a) dU = 0

(b) dQ = 0

(d) dQ = dW

Choose the correct alternatives:

1. (a, b, c)

2. (a, d)

3. (b, c, d)

4. (a, c, d)

(1, 4) Hint: In isothermal processes, the change in temperature is equal to zero.

Step 1: Find the change in the internal energy of the gas.

For an isothermal process change in temperature of the system,

∆

T =0

\Rightarrow

T =constant.
We know that for an ideal gas, dU = change in internal energy = n

C_{v}

∆

T = 0
[where n is the number of moles and C is the specific heat capacity at constant volume]

Step 2: Use the first law of thermodynamics.
From the first law of thermodynamics,

dQ = dU + dW

= 0 + dW

\Rightarrow

dQ = dW