Question

A 65 g block of metal absorbs 5850 J of heat energy and the temperature of the block rises from 10 degrees Celsius to 41 degrees Celsius. What is the specific heat capacity of the metal?

Answer 1

Q224396

A 65 g block of metal absorbs 5850 J of heat energy and the temperature of the block rise from 10 degrees Celsius to 41 degrees Celsius. What is the specific heat capacity of the metal?

Solution :

We are given the mass of the metal block, the block's initial temperature, and the block's final temperature after absorbing 5850 Joules of heat energy.

mass of metal block, m = 65 g

Initial temperature, T_i = 10 ^oC

Final temperature, T_f = 41 ^oC

Heat absorbed by the block, Q = 5850 Joules.

specific heat capacity of the metal, s = unknown

$Q = m \ s \ \Delta T$

$\Delta T = T_f - T_i = 41^o C - 10 ^o C = 31 ^o C$

plug all the information in the formula and solve for 's'.

$$5850 \ J = 65 g \ * s * \ 31 ^o C$$

$$5850 \ J = 2015 \ g \ ^o C \ * \ s$$

dividing both the side by 2015 g oC, we have

$$\frac{5850 \ J}{2015 \ g \ ^o C } = \frac{\cancel{2015 \ g \ ^o C } \ * \ s }{\cancel{2015 \ g \ ^o C }}$$

$$\frac{5850 \ J}{2015 \ g \ ^o C } = \ s$$

$$2.903 \ J /g ^o C = \ s$$

In the correct significant figure the answer is 2.9 J/g ^oC.

Hence the specific heat capacity of the metal is 2.9 J/g ^oC.