Thermodynamics Questions

One kg of a diatomic gas is at a pressure of $8\times 10^4{\text{N/m}}^2$. The density of the gas is $4{\text{kg/m}}^3$. What is the energy of the gas due to its thermal motion?

Directions: Question numbers 28, 29 and 30 are based on the following paragraph. Two moles of helium gas are taken over the cycle ABCDA, as shown in the P – T diagram.

Two moles of helium gas are taken over the cycle $ABCDA$, as shown in the $P–T$ diagram. Assuming the gas to be ideal, the work done on the gas in taking it from $A$ to $B$ is:

Referring to the $P–T$ diagram in the previous question, the work done on the gas in taking it from $D$ to $A$ is:

Referring to the $P–T$ diagram, the net work done on the gas in the cycle $ABCDA$ is:

In a fuel cell methanol is used as fuel and oxygen gas is used as an oxidizer. The reaction is ${\text{CH}}_3\text{OH}(l)+\frac{3}{2}{\text{O}}_2(g)\to {\text{CO}}_2(g)+2{\text{H}}_2\text{O}(l)$. At $298\text{K}$ standard Gibb’s energies of formation for ${\text{CH}}_3\text{OH}(l)$, ${\text{H}}_2\text{O}(l)$ and ${\text{CO}}_2(g)$ are $-166.2$, $-237.2$ and $-394.4{\text{kJ mol}}^{-1}$ respectively. If standard enthalpy of combustion of methanol is $-726{\text{kJ mol}}^{-1}$, efficiency of the fuel cell will be: