Question

A 55-g copper calorimeter (c=0.093calcal/g·° C) contains 250 g of water at 18.0° C. When 75 g of an alloy at 100° C is dropped into the calorimeter, the resulting temperature is 20.4° C. What is the specific heat of the alloy?

Answer 1

To find the specific heat of the alloy, we can use the formula Q=mcΔT. By applying this formula to the given information and solving for the specific heat of the alloy, we find that it is approximately 0.114 cal/g·°C.

Step-by-step explanation:

To find the specific heat of the alloy, we can use the formula:
Q = mcΔT

Where Q is the heat gained or lost, m is the mass of the substance, c is the specific heat of the substance, and ΔT is the change in temperature.

First, we can calculate the heat gained by the water:
Qwater = mwater cwater ΔTwater
Qwater = (250 g) (1 cal/g·°C) (20.4°C - 18.0°C) = 480 cal

Next, we can calculate the heat lost by the alloy:
Qalloy = malloy calloy ΔTalloy
Qalloy = (75 g) (calloy) (20.4°C - 100°C) = -808.2 cal

Since energy is conserved in the system, the heat gained by the water is equal to the heat lost by the alloy:
Qwater = -Qalloy
480 cal = 808.2 cal
calloy = -808.2 cal / (75 g * (20.4°C - 100°C)) = 0.114 cal/g·°C

The specific heat of the alloy is approximately 0.114 cal/g·°C.