Question

A balloon of 20 cm diameter is filled with air at 1.2 bar and ${25}^{\circ }C$ It is heated to ${700}^{\circ }C$ and as a result its diameter increases to 25 cm. The variation of pressure Vs diameter during heating is shown below, rising to a maximum value of 1.5 bar. The heat transferred to the balloon if the energy change of air $\Delta E$ is given by $\Delta E=3\Delta T$ Joule, where $\Delta T$ is the change in temperature in kelvin is _____ J

• A. 2568 J
• B. 2400J
• C. 255J
• D. 2453J

Answer 1

The correct option is A 2568 J


The variation of P is D can be given as

$P=1.2+6(D-0.2)=6D$

$W=\int Pdv\left(\text{Since work is done on air}\right)$

$=-{\int }_{0.2}^{0.25}6Ddv$

$W_{on}=-{\int }_{0.2}^{0.25}6D\times \frac{\pi D^2}{2}dD=\frac{3\pi }{4}(D^4{)}_{0.2}^{0.25}$

$=-5.434\times {10}^{-3}\text{bar-}{m}^3=-543.4J$

$\text{The change in energy,}\Delta E=3\Delta T$

$=3(700-25)=2025J$

$\text{Now using first law}{Q}_{in}=\Delta E-W_{on}=2025-(-543.4)$

$=2568J$