Question

(a)Find the energy absorbed as heat and (b) Find the change in entropy of a 2.00 kg block of copper whose temperature is increased reversibly from $\mathbf{25}\mathbf{.}\mathbf{0}\mathbf{°}\mathit{C}$torole="math" localid="1661323309034" $\mathbf{100}\mathbf{°}\mathit{C}$. The specific heat of copper is 386 J/kgK.

Short answer

1. The amount of energy absorbed as heat is$579\times {10}^{4}J$
2. The change in entropy of block of copper is$173.3J/K$

Step-by-step solution

The given data

1. Mass of the block of copper, m = 2 kg
2. Initial temperature of copper,$T_i={25}^{0}Cor298K$
3. Final temperature of copper, $T_f={100}^{0}Cor373K$
4. Specific heat of copper,$c_{copper}=386J/kgK$

Understanding the concept of heat and entropy change of reversible process

Using the given data, the formula for the energy absorbed in the form of heat, we can get the required amount of energy for the required change. Again, using the formula of the entropy change for a reversible process at constant volume change, we get the required change in entropy of the gas.

Formulae:

The energy absorbed as heat by the gas, $Q=mc∆T$ …(i)

The entropy change of a gas, $∆S=mc\ln \left(\frac{T_f}{T_i}\right)$ …(ii)

(a) Calculation of the absorbed energy by the block of copper

Substituting the given values in equation (i), we can get the amount of energy absorbed by the block of copper as follows:

$$\begin{gathered} Q=\left(2kg\right)\left(386J/kgK\right)\left[\left(373-298\right)K\right] \\ =5.79\times {10}^{4}J \end{gathered}$$

Hence, the required value of the energy that is absorbed by the block is$5.79\times {10}^{4}J$

(b) Calculation of the change in entropy of the block of copper

Substituting the given data in equation (ii), the entropy change of the copper block is given as follows:

$$\begin{gathered} ∆S=\left(2kg\right)\left(386J/kgK\right)\ln \left(\frac{373K}{298K}\right) \\ =173.3J/K \end{gathered}$$

Hence, the value of the entropy change is 173.3 J/K