Question

9.5J of heat is required to increase the temperature of 3 moles of gas from 40°C to 47°C at constant volume. The amount of heat required to raise the same
temperature at constant pressure will be:
(Take R = 0.2 J/Kg K)
Ops: A.
B.
C
D.
13.65 )
13.45 J
13.55 )
13.75 )​

Answer 1

Given that,

Heta = 9.5 J

Number of moles =2

Initial temperature = 40°C

Final temperature = 47°C

We need to calculate the value of $c_{v}$

Using formula of heat

$Q=nc_{v}\Delta T$

$c_{v}=\dfrac{Q}{n\Delta T}$

Put the value into the formula

$c_{v}=\dfrac{9.5}{3\times(47-40)}$

$c_{v}=0.452$

We need to calculate the value $c_{p}$

Using formula of R

$c_{p}-c_{v}=R$

$c_{p}=R+c_{v}$

Put the value into the formula

$c_{p}=0.2+0.452$

$c_{p}=0.652$

We need to calculate the amount of heat required to raise the same  temperature at constant pressure

Using formula of heat

$Q'=nc_{p}\Delta T$

Put the value into the formula

$Q'=3\times 0.652\times7$

$Q'= 13.65\ J$

Hence, The amount of heat required to raise the same  temperature at constant pressure is 13.65 J.

(A) is correct option.