Question

A 110mm diameter cylinder contains 100cm3 of water at 60°C. A 50kg piston sits on top of the water. If heat is added until the temperature is 200°C, find the work done.

Answer 1

The work is given by formula

$$A=p(V_2 - V_1) (1)$$

where p is the pressure

We can write for force balance in cylinder

$$mg=pS – p_{atm} S (2)$$

where m=50kg, g=10 N/kg, p_atm=10⁵ Pa

Area of the piston is equal to

$$S=\frac { \pi d^2} {4} (3)$$

We put (3) in (2) and get: p=151600 Pa

Gay-Lussac's law is given by formula

$$\frac {V_1} {V_2} = \frac {T_1} {T_2} (4)$$

where V₁=0.0001 m³, T₁=333 K, T₂=473 K

Using (4) we get: V₂=0.142 m³

According to formula (1), we calculate the work:

A=21.5 kJ

Answer:

21.5 kJ