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

Step-by-step 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

`(P_i)/(T_i)`=
`(P_f)/(T_f)`

`(14.7)/(70)`=
`(30)/(T_f)`

`T_f=142.85^(\circ)F`

volume of canister=
`\pi * r^(2)* h`

=
`\pi * 5^(2)* 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* 10^(-3)* \left ( 142.857-70\right )`

=1539.052J=1.458Btu