$0.120 k g$ of copper of specific heat capacity $100 c a l k g^{- 1} ° C^{- 1}$ and at $20 ° C$ is heated by a burner for two minutes, which supplies heat energy at the rate of $20 c a l o r i e s / s e c$ . Calculate the final temperature of copper.

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Solution

Step 1: Given data
Mass $(m) = 0.120 k g$
Specific heat capacity $(c) = 100 c a l k g^{- 1} ° C^{- 1}$
Rate of heat energy supplied $= 20 c a l o r i e s / s e c$
Time $(t) = 2 m i n u t e s = 120 s e c o n d s$
Initial temperature $T_{1} = 20 ° C$
Final temperature $T_{2} = ?$
Rise in temperature $(θ_{R}) = T_{2} - T_{1}$
Step 2: Calculating the total heat supplied and then rise in temperature
Total heat supplied to copper= Rate of heat energy supplied $\times$ Time
$= 20 c a l / s \times 120 s = 2400 c a l$
Step 3: Calculating the rise in temperature
Now, total heat supplied $= m c θ_{R}$
$\Rightarrow 2400 c a l = 0.120 k g \times 100 c a l k g^{- 1} ° C^{- 1} \times θ_{R} \Rightarrow θ_{R} = \frac{2400}{0.120 \times 100} \Rightarrow θ_{R} = 200 ° C$
Step 4: Calculating the final temperature of copper
We know,
$θ_{R} = T_{2} - T_{1} = 200 ° C T_{2} = 200 ° C + T_{1} T_{2} = 200 ° C + 20 ° C T_{2} = 220 ° C$
The final temperature of copper is $220 ° C$ .

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0.120kg of copper of specific heat capacity 100calkg-1°C-1and at 20°C is heated by a burner for two minutes, which supplies heat energy at the rate of 20calories/sec. Calculate the final temperature of copper.

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