SPRING 2002 QUIZ 6

PHYSICS 100A 

1.  0.2kg ice is originally at -10°C. How much heat is needed to completely melt the ice at 0°C?

Solution.

The ice needs to rises its temperature from -10°C to 0°C first.

We find the heat needed from

                     Q = m_icec_iceDT_ice + m_iceL_ice

                        = (0.2kg)(2100J/kg·C°)[0 - (-10°C)] + (0.2kg)(3.33 x 10⁵J/kg)

                        = 7.08 x 10⁴J.

2. An ideal gas is isobarically expands its volume from 3.00m³ to 5.00m³ under pressure of 2.00atm, then it is isochorically compressed to its original temperature. Calculate (a) the change in internal energy of the gas, and (b) the heat absorbed during the process.

Solution.

The gas does work only during the isobaric process. We find the work done from

                         W = PDV

                             = (2.00atm)(1.013 x 10⁵N/m²)(5.00m³ - 3.00m³)

                             = 4.05 x 10⁵J.

(a) Because during the process the temperature of the gas is unchanged, we have DU = 0.

(b) According to the first law of thermodynamics, we have

                        DU = Q - W;

                           0 = Q - 4.05 x 10⁵J, which gives Q = 4.05 x 10⁵J.