# In a experiment it is observed that 252 J of heat must be absorbed to raise the temperature of 50.0 g of Ni(s) from 20.0 C to 31.4 C. How do you calculate the specific heat of Ni in both J/g °C and cal/g.C?

Nov 24, 2016

Using Joules, the specific heat of nickel is 0.442 "J"/("g"^@*"C").

Using calories, the specific heat of nickel is 0.106"cal"/("g"^@*"C"). in calories.

#### Explanation:

The equation to use is $Q = m c \Delta T$, where $Q$ is the energy in Joules, $m$ is the mass, $c$ is the specific heat, and $\Delta T$ is the change in temperature. $\Delta T = {T}_{\text{final"-T_"initial}}$

$Q = \text{252 J}$
$m = \text{50.0 g}$
$\Delta T = \text{31.4"^@"C"-"20.0"^@"C"="11.4"^@"C}$
c=???

Rearrange the equation to isolate $c$. Add the given values and solve.

$c = \frac{Q}{m \cdot \Delta T}$

$c = \left(252 \text{J")/((50.0"g")(11.4^@"C}\right)$=0.442 "J"/("g"^@"C")

Convert Joules to calories.

$\text{1 J=0.239"cal}$

$0.442 \cancel{\text{J"xx(0.239"cal")/(1cancel"J")="0.106 cal}}$

Using Joules, the specific heat of nickel is 0.442 "J"/("g"^@*"C").

Using calories, the specific heat of nickel is 0.106"cal"/("g"^@*"C"). in calories.