Question

To understand the concepts of heat capacity, specific heat, andmolar heat capacity.
Heat capacity, C, is the amount of energy required to raise thetemperature of a substance by exactly 1 degree Celsius. The energyneeded to warm an object increases as the mass of that objectincreases. We see this in our everyday life. For example, we knowthat it takes much more energy to heat a large tank of water than asmall cup. Because of this dependence on mass, experimentallydetermined heat capacities are always reported in terms of theamount of the substance that is heated. One method is to report howmuch energy it takes to raise the temperature of one mole of asubstance by exactly 1 degree Celsuis. This value is the molar heatcapacity, which has the symbol C_p.The molar heat capacity is givenin the units \rm J / mol \cdot{}^\circ C. A second method is toreport how much energy it takes to raise the temperature of onegram of a substance by exactly 1 degree Celsius. This value is thespecific heat, which has been given the symbol C_s. The units forspecific heat are \rm J / g \cdot{} ^\circ C.

The heat capacity of a substance is therefore related to the energyq needed to raise its temperature by an amount Delta T. That is, q= nC_{\rm p}\Delta T, where n denotes the number of moles of thesubstance, or q = mC_{\rm s}\Delta T, where m denotes the number ofgrams of the substance.

Part A
It takes 53.0 J to raise the temperature of an 8.10 g piece ofunknown metal from 13.0 C to 24.0 C. What is the specific heat forthe metal?
Express your answer numerically, J/g*C

Part B
The molar heat capacity of silver is 25.35 j/mol*C. How much energywould it take to raise the temperature of 8.10 g of silver by 13.8C?

Part C
What is the specific heat of silver?