Question

The percentage increase in temperature of a gas when it is heated at constant pressure to increase the volume by 30% is
a) 20%
b) 30%
c) 23.08%
d) 40.15%

Answer 1

answer : option (b) 30%

explanation : at constant pressure,

volume is directly proportional to temperature of gas.

e.g., $V\propto T$

so, $\frac{V_1}{T_1}=\frac{V_2}{T_2}$ .........(1)

a/c to question,

volume increases, ∆V = 30%

Let initial volume is V

then, final volume will be V + 30%of V = 1.3V

Let initial temperature is T

from equation (1),

V/T = 1.3V/T'

or, T' = 1.3T

so, % change in temperature = (1.3T - T)/T × 100 = 30%

hence, option (b) is correct

Answer 2

From ideal gas equation we know that ,

pv=nRT                              (where p= pressure

                                                       v=volume

                                                       nR=constant

                                                        T=temperature)

At constant pressure v∝T

So, as v increases, T also increases by the same amount

Therefore Temprature will increase by 30%