Certain amount of heat is given to 100 g of copper to increase its temperature by `21^@C`. If same amount of heat is given to 50 g of water, then the rise in its temperature is (specific heat capacity of copper ` = 400 J kg^(-1) K^(-1)` and that for water ` = 4200 J kg^(-1) K^(-1))`

Options

A. `4^(@)C`
B. `5.25^(@)C`
C. `8^(@)C`
D. `6^(@)C`

Answer

A

Explanation

Here, mass of copper, `m_(Cu) = 100g = 100 xx 10^(-3) kg`
Specific heat capacity of copper `s_(Cu) = 400J kg^(-1) K^(-1)`
Mass of water, `m_(w) = 50 g = 50 xx 10^(-3) kg`
Specific heat capacity of water, `s_(w) = 4200 J kg^(-1) K^(-1)`
The amount of heat required to increase the temperature of copper by `21^(@)C` is
`Q= m_(Cu) s_(Cu) Delta T= 100 xx 10^(-3) xx 400 xx 21J`
The amount of heat required to increase the temperature of water by `Delta T_(1) ""^(@)C` is
`Q_(1) = m_(w) s_(w) Delta T_(1) = 50 xx 10^(-3) xx 4200 xx Delta T_(1)`
According to the given problem, `Q= Q_(1)`
`:. 100 xx 10^(-3) xx 400 xx 21 = 50 xx 10^(-3) xx 4200 xx Delta T_(1)`
or `Delta T_(1) = (2 xx 4 xx 21)/(42) = 4^(@)C`