In a monatomic ideal gas the pressure and volume relation follows the equation given by P6 V5 = constant. The gas contains n number of moles. Find out amount of heat required to increase the temperature of gas by 5 kelvin.

Question

In a monatomic ideal gas the pressure and volume relation follows the equation given by P6 V5 = constant. The gas contains n number of moles. Find out amount of heat required to increase the temperature of gas by 5 kelvin. (A) 15 nR (B) 7.5 nR (C) 75 nR (D) 37.5 nR

Tardigrade Admin · Accepted Answer

P6 V5 = const ⇒ PV (5/6)=const. Now C = Cv + (R/1-x)= (3/2) R + (R/1- (5)6)= (15R/2) Heat supplied , Q = n C Δ T = n ( (15R/2))(5)=37.5 nR

Q. In a monatomic ideal gas the pressure and volume relation follows the equation given by $P^{6} V^{5}$ = constant. The gas contains n number of moles. Find out amount of heat required to increase the temperature of gas by 5 kelvin.

15 nR

7.5 nR

75 nR

37.5 nR

$P^{6} V^{5} = co n s t$
$\Rightarrow P V^{\frac{5}{6}} = co n s t .$
$N o w C = C_{v} + \frac{R}{1 - x} = \frac{3}{2} R + \frac{R}{1 - \frac{5}{6}} = \frac{15 R}{2}$
Heat supplied , $Q = n C Δ T$
= $n (\frac{15 R}{2}) (5) = 37.5 n R$

Q. In a monatomic ideal gas the pressure and volume relation follows the equation given by P6V5 = constant. The gas contains n number of moles. Find out amount of heat required to increase the temperature of gas by 5 kelvin.