Heat is added to 10^3 cubic cm of water at atmospheric pressure. The water's temperature increases by 50 degrees celsius. Find (a) the work done by the water as it expands (b) the increase in water's internal energy.

Workdone = P ΔV 

 

where P = 1.01 × 10⁵ Pa  is pressure that is kept constant during expansion and ΔV is change in volume

 

ΔV = V_i β ΔT  

 

where V_i = 10³ × 10^-6 m³  is initial volume , β = 210 × 10^-6 /°C is volume expansion coefficient and ΔT = 50 °C is change in temperature .

 

ΔV = 10³ × 10^-6 × 210 × 10^-6 × 50 = 1.05 × 10^-5 m³ 

 

Workdone = P ΔV = 1.01 × 10⁵ × 1.05 × 10^-5 = 1.060 J

 

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Chane in internal energy ΔU = m C_p ΔT

 

where m is mass of water , C_p is specific heat and ΔT is change in temperature

 

mass of water m = volume × density = 10³ × 10^-6 × 1000 = 1 kg

 

Chane in internal energy ΔU =1 × 4186 × 50 = 2.093 × 10⁵ J  = 209.3 kJ