Ncert Exercises & Solutions

An ideal gas undergoes an isothermal process from some initial state

i

$i$ to the final state

𝑓

$𝑓$ .

(a)	$dU = 0$	(b)	$dQ = 0$
(c)	$dQ = dU$	(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

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

C_{v}

$C_{v}$

∆

$∆$ 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

$\Rightarrow$ dQ = dW