JEE Main · 2017 · 02 Apr 2017 · Offline · Heat & Thermodynamics

The temperature of an open room of volume

30 m^{3}

increases from

1 7^{\circ} C

2 7^{\circ} C

due to the sunshine. The atmospheric pressure in the room remains

1 \times 1 0^{5} Pa

. If

n_{i}

and

n_{f}

are the number of molecules in the room before and after heating, then

n_{f} - n_{i}

will be :

Answer: (B)

Solution

At fixed pressure and volume the molecule count obeys

n = \frac{P V}{k T}

, so warming the open room drives molecules out of the door. The change is

n_{f} - n_{i} = \frac{P V}{k} (\frac{1}{T _{f}} - \frac{1}{T _{i}}) = \frac{1 0 ^{5} \times 30}{1.38 \times 1 0 ^{- 23}} (\frac{1}{300} - \frac{1}{290})

. With

T_{f} > T_{i}

the bracket is negative, and the arithmetic yields about

- 2.5 \times 1 0^{25}

. The minus sign is the physics: the hotter room holds fewer molecules.

JEE Main · 2017 · 02 Apr 2017 · Offline · Single correct option