7. The specific heat capacity of a body with a mass of $m=2$ kg depends on the temperature as follows: $c=c_{0}(1+\alpha t)$, where $c_{0}=150$ J/kg ${ }^{\circ} \mathrm{C}-$ specific heat capacity at $0^{\circ} \mathrm{C}, \alpha=0.05^{\circ} \mathrm{C}^{-1}$ - temperature coefficient, $t$ - temperature in degrees Celsius. Determine the amount of heat that must be transferred to this body to heat it from $20^{\circ} \mathrm{C}$ to $100^{\circ} \mathrm{C}$. (10 points)
Answer: 96 kJ

Solution. Given that the specific heat capacity depends linearly on temperature, we can calculate its average value: $c_{c p}=\frac{c_{0}\left(1+\alpha t_{h}\right)+c_{0}\left(1+\alpha_{\kappa}\right)}{2}=600 \frac{\text { J }}{\text { kg } \cdot{ }^{\circ} \mathrm{C}} \quad(5$ points). The required amount of heat: $Q=c_{\varphi} m \Delta t=600 \cdot 2 \cdot 80=96000$ J = 96 kJ (5 points $)$.