**Problems**

1. A precious-stone dealer wishes to find the specific heat capacity of a 0.030-kg gemstone. The specimen is heated to 95.0°C and then placed in a 0.15-kg copper vessel that contains 0.080 kg of water at equilibrium at 25.0°C. The loss of heat to the external environment is negligible. When equilibrium is established, the temperature is 28.5°C. What is the specific heat capacity of the specimen?

2. Blood can carry excess energy from the interior to the surface of the body, where the energy is dispersed in a number of ways. While a person is exercising, 0.6 kg of blood flows to the surface of the body and releases 2000 J of energy. The blood arriving at the surface has the temperature of the body interior, 37.0°C. Assuming that blood has the same specific heat capacity as water, determine the temperature of the blood that leaves the surface and returns to the interior.

3. At a fabrication plant, a hot metal forging has a mass of 57 kg and a specific heat capacity of 430 J/(kg · C°). The final temperature of the oil and forging at thermal equilibrium is 47 °C. Assuming that heat flows only between the forging and the oil, determine the initial temperature of the forging.

4. When resting, a person has a metabolic rate of about 4.2 X 10⁵ joules per hour. The person is submerged neck-deep into a tub containing 1.0 X 10³ kg of water at 27.00 °C. If the heat from the person goes only into the water, find the water temperature after half an hour.

5. In a passive solar house, the sun heats water stored in barrels to a temperature of 38 °C. The stored energy is then used to heat the house on cloudy days. Suppose that 2.4 X 10⁸ J of heat are needed to maintain the inside of the house at 21 °C. How many barrels (1 barrel = 0.16 m³) of water are needed?

6. An electric hot water heater takes in cold water at 13.0 °C and delivers hot water. The hot water has a constant temperature of 45.0 °C, when the "hot" faucet is left open all the time and the volume flow rate is 5.0 X 10^-6 m³/s. What is the minimum power rating of the hot water heater?