Question

1. A 170 g copper bowl contains 110 g of water, both at 23.0°C. A very hot 370 g copper cylinder is dropped into the water, causing the water to boil, with 4.17 g being converted to steam. The final temperature of the system is 100°C. Neglect energy transfers with the environment. (a) How much energy is transferred to the water as heat? (b) How much to the bowl? (c) What is the original temperature of the cylinder? The specific heat of water is 1 cal/g·K, and of copper is 0.0923 cal/g·K. The latent heat of vaporization of water is 539 Cal/kg.

2. One liter of a gas with γ = 1.30 is at 369 K and 1.98 atm pressure. It is suddenly compressed adiabatically to 1/9 its original volume. (a) Find its final pressure and (b) temperature. (c) The gas is now cooled back to 369 K at constant pressure. What is its final volume?

Answer 1

1.(a)

Total heat transfer to water = 100 g of water temp changed to + 4.17 g into steam.

Energy = 100*1*(100-23) + 4.17*539 = 9947.63 Cal

1.(b)

Energy to bowl = = 170*0.0923*(100-23) = 1208.207 Cal

1.(c)

Conservation of energy

Energy from copper cylinder = Energy to bowl + Energy to water

370*0.0923*(T - 100) = 1208.207 +9947.63 = 11155.837

T-100 = 326.66

T=

2 Adiabatic process,

  

2.(a)

atm

2.(b)

  

2.(c)

V/T = constant

T2 = 713.34 K

V1 = 1/9 of the original volume = 1/9 litre

final volume = 19.3*(1/9) = 2.14 litre