Question

A rigid canister with a radius of 5 in and a height of 10 in is filled with air. The initial pressure and temperature of air in the canister are 14.7 psi and 70 °F respectively. Later, the canister is heated such that the air pressure inside it, increases to 30 psi. Calculate the total heat transferred in [Btu] to air in the canister during this process.

Answer 1

Answer:1.458 Btu

Explanation:

Given

radius of canister$\left ( r\right )=5in$

Height of canister$\left ( h\right )=10 in.$

Initial pressure$\left ( P_i\right )=14.7 Psi$

Initia ltemprature$\left ( T_i\right )=70^{\circ}F$

Final pressure$\left ( P_f\right )=30Psi$

as canister is rigid therefore change in volume is zero

therefore

$\frac{P_i}{T_i}$=$\frac{P_f}{T_f}$

$\frac{14.7}{70}$=$\frac{30}{T_f}$

$T_f=142.85^{\circ}F$

volume of canister=$\pi \times r^{2}\times h$

                               =$\pi \times 5^{2}\times 10=250\pi$

volume of canister=12872,038.8 $mm^3$

now calculating mass of air

PV=mRT

substituting values

$\left ( 14.7Psi\right )\left ( 12872,038.8 mm^3\right )=m\left ( 0.287\right )\left ( 70^{\circ}F\right )$

m=21.0192 gm

Therefore heat transferred =$mc_p\left ( T_f-T_i\right )$

                                             =$21.0192\times 10^{-3}\times \left ( 142.857-70\right )$

                                             =1539.052J=1.458Btu