Question

In a monoatomic ideal gas the pressure and volume relation follow the equation given by p6 v5=constant.the gas contain n no. of moles.fine out the amount of heat required to increase the temperature of gas by 5 kelvin​

Answer 1

Given:

In a monoatomic ideal gas the pressure and volume relation follow the equation given by P^(6)V^(5)=constant. The gas contain n no. of moles.

To find:

Heat required to increase temperature by 5 K.

Calculation:

${P}^{6} {V}^{5} = constant$

$= > P {V}^{ \frac{5}{6} } = c$

Now , the Specific Molar Heat capacity:

$C = C_{v} + \dfrac{R}{1 - n}$

$= > C = \dfrac{3R}{2} + \dfrac{R}{(1 - \frac{5}{6}) }$

$= > C = \dfrac{3R}{2} + \dfrac{R}{( \frac{1}{6}) }$

$= > C = \dfrac{3R}{2} + 6R$

$= > C = \dfrac{15R}{2}$

Now, required heat will be Q:

$Q = n \times C \times d \theta$

$= > Q = n \times \dfrac{15R}{2} \times5$

$= > Q = \dfrac{75nR}{2}$

So, final answer is:

$\boxed{ \bold{ \blue{ \large{ Q = \dfrac{75nR}{2} }}}}$