Consider an ideal gas contained in a cylinder that can do work by pushing against a piston, which has a surface area of 100 cm2 . a. If 10 Btu/min of heat is transferred to the gas for 4 minutes during a constant volume process, what is the total change in internal energy? Express answer in kJ. b. Now suppose that the pressure inside the cylinder is a constant 20 atm, a total of 30 Btu of heat is transferred to the gas, and the gas displaces the piston 15 cm upwards. What is the change in internal energy? Express answer in kJ.

a. ΔU = 42.2 KJ

b. ΔU = 34689.75 J = 34.7 KJ

Explanation:

a.

For a constant volume process:

ΔQ = ΔU

where,

ΔQ = Heat Supplied to the system

ΔU = Change in internal energy

but.

ΔQ = (Heat Transfer Rate)(Time Duration)

ΔQ = (10 Btu/min)(4 min)

ΔQ = (40 Btu)(1.055 KJ/1 Btu)

ΔQ = 42.2 KJ

Therefore, the equation becomes:

ΔU = 42.2 KJ

b.

For a constant pressure process:

ΔQ = ΔU + PΔV

ΔU = ΔQ - PΔV

where,

ΔV = Change in volume = (Surface Area)(Displacement) = (100 cm²)(15 cm)

ΔV = (1500 cm³)(10⁻⁶ m³/1 cm³) = 1.5 x 10⁻³ m³

P = Pressure = (20 atm)(101325 Pa/1 atm) = 2.0265 x 10⁶ Pa

ΔQ = Heat transferred to Gas = (30 Btu)(1055 J/1 Btu) = 31650 J

ΔU = Change in Internal Energy = ?

Therefore,

ΔU = 31650 J + (2.0265 x 10⁶ Pa)(1.5 x 10⁻³ m³)

ΔU = 31650 J + 3039.75 J

ΔU = 34689.75 J = 3.47 KJ