Radioactive decay of granite and other rocks in Earth's interior provides sufficient energy to keep the interior molten, to heat lava, and to provide warmth to natural hot springs. This is due to the average release of about 0.03 J per kilogram each year. Find an increase in temperature for a thermally insulated chunk of granite that takes about 13.4 million years to change temperature. (Assume that the specific heat capacity c of granite is 800 J/kg⋅C∘. Use the equation Q=cmΔT.)

When it rains, water vapor in the air condenses into liquid water, and energy is released. (a) How much energy is released when 0.0318 m (1.25 inch) of rain falls over an area of 2.59×106 m² (one square mile)? (b) If the average energy needed to heat one home for a year is 1.50x1011 J, how many homes could be heated for a year with the energy determined in part (a)? (a) Number (b) Number i i Units Units >

Ice at 0 °C is placed in a Styrofoam cup containing 0.62 kg of lemonade at 32 °C. The specific heat capacity of lemonade is virtually the same as that of water; that is, c = 4180 J/(kg C°). After the ice and lemonade reach an equilibrium temperature, some ice still remains. The latent heat of fusion for water is Lf = 3.35 x 105 J/ kg. Assume that the mass of the cup is so small that it absorbs a negligible amount of heat, and ignore any heat lost to the surroundings. Determine the mass of ice that has melted, in grams.

A chunk of metal with a mass of 85.0 grams and a specific heat of 759 joules per kilogram·kelvin is heated to 78.9 degrees Celsius and placed in 122 milliliters of water (c = 4186 J/kg·K) at 18.6 degrees Celsius. What is the final temperature of the metal and water? Hint: The heat lost by the metal is gained by the water, so the sum of the heats is zero.

Note: Round off your answer up to 3 decimal places.  Input only the numerical value. Researchers are conducting a study to quantity the thermal conductivity of a composite material. A square box is made from 838 cm2 sheets of the composite insulating material that is 2.8 cm thick. A 201 W heater is placed inside the box. Sensors attached to the box show that the interior and exterior surfaces of one face have reached the constant temperatures of 81°C and 38°C. What is the thermal conductivity in W/m-K?

Consider a 10.0 kg iron box holding 48.0 kg of solid ice. Initially, both the box and the ice are at −35.0 ̊C. You put the box on an electric heater, which has a power output of 9580 Watts. Assume that all of the energy produced by the heater goes into heating the box and the ice. The specific heat of iron is 450.0 J kg−1 ̊C−1, the specific heat of ice is 2108 J kg−1 ̊C−1, and the latent heat of fusion of ice is 333500 J kg−1. (a)How much energy is required to heat the box and the ice to the melting point of ice (0 ̊C)? Give your answer in Joules. (b)How much energy (in Joules) is required to then melt all of the ice?

Rubbing your hands together warms them by converting work into thermal energy. If a woman rubs her hands back and forth for a total of 10 rubs, at a distance of 7.50 cm per rub, and with a frictional force of 50.0 N, what is the temperature increase in degrees Celsius? The mass of tissue warmed is only 0.100 kg, mostly in the palms and fingers.

An ice block of mass 1.2000000000000002 kg at an initial temperature of –11 ∘C is put into a copper pot of mass 2.5 kg containing 4.3 L of water at 21 ∘C. If you heat up the pot, what is the amount of energy (in J) you need to convert all the ice and the water into steam? (Assume that no energy is lost from the system.)   You may need some or all of the following constants: The specific heat of ice is 2200 J/kg ∘C, the specific heat of copper is 386 J/kg ∘C and the specific heat of water is 4186 J/kg ∘C. The latent heat of fusion of ice is 334000 J/kg and the heat of vaporization for water is 2256000 J/kg .