The temperature of 100 g of water is to be raised from 30 °C to 90 °C by adding steam to it. The mass of steam required to raise this temperature will be nearly (Take, \(S_W = 1\) cal/g °C, \(L = 540\) cal/g):
Heat gained by water = \(100 \times 1 \times (90-30) = 6000\) cal. Heat lost by steam = \(m \times 540 + m \times 1 \times (100-90) = 550m\). Equating gives \(m \approx 11\) g.
When 150 gm of ice at \( 0^\circ\text{C} \) is mixed with 60 gm of water at \( 50^\circ\text{C} \) in a container, the resulting temperature is
Heat lost by water to cool to \( 0^\circ\text{C} \) is \( Q_{\text{lost}} = m_w c_w \Delta T = 60 \times 1 \times 50 = 3000 \text{ cal} \). Heat needed to melt all ice is \( Q_{\text{melt}} = m_i L = 150 \times 80 = 12000 \text{ cal} \). Since \( Q_{\text{lost}} < Q_{\text{melt}} \), only a part of the ice melts, and the final temperature remains \( 0^\circ\text{C} \).
1 g of steam at 100°C is mixed with 1 g of ice at 0°C, then resultant temperature of the mixture is
Heat required to raise 1 g of ice at 0°C to water at 100°C is \(1 \times 80 + 1 \times 1 \times 100 = 180\text{ cal}\). Since 1 g steam releases \(540\text{ cal}\) upon complete condensation, only a fraction of the steam condenses, maintaining the final temperature at 100°C.
Assertion (A): Specific heat of substance is property of material.
Reason (R): Specific heat also depends on the condition of the experiment. The way in which heat is supplied to the body.
Specific heat is an intrinsic property of a substance, dependent only on the material itself and its phase, not on experimental conditions or how heat is supplied. Thus, Assertion (A) is true. Reason (R) is false. Therefore, (A) is true but (R) is false.
Assertion (A): Specific heat for melting Ice is infinite.
Reason (R): In isothermal process specific heat of substance is infinite.
Specific heat is defined as \(c = \frac{Q}{m \Delta T}\). During melting (a phase change), the temperature \(\Delta T\) remains constant, meaning \(\Delta T = 0\). Hence, the specific heat \(c\) becomes infinite. Both assertion and reason are true, and the reason explains the assertion.
Assertion (A): Specific heat for melting Ice is infinite.
Reason (R): In isothermal process specific heat of substance is infinite.
Specific heat is \(C = \frac{Q}{m \Delta T}\). During melting, \(\Delta T = 0\), so \(C\) is infinite. Melting is an isothermal process, so both A and R are true and R explains A.
Assertion (A): Two bodies at different temperatures, if brought in contact do not necessary settle to the mean temperature.
Reason (R): The two bodies may have different thermal capacities.
The final temperature of two bodies in contact depends on their thermal capacities \(m\times c\). If capacities are unequal, the final temperature will not be the mean. Both A and R are true, and R explains A.
Assertion (A): During phase change temperature of the substance remains constant.
Reason (R): Internal energy of the substance during change of phase remains constant.
Assertion (A) is true; temperature is constant during phase change. Reason (R) is false; internal energy changes as latent heat is absorbed/released to alter molecular potential energy.
Assertion (A): An ice skater can slide over ice smoothly if the skate blades are sharp.
Reason (R): Melting point of ice decreases with increase in pressure.
Sharp blades increase pressure, lowering ice's melting point (regelation). A thin water layer forms, reducing friction, allowing smooth sliding. Thus, R correctly explains A.
Assertion (A): Water can be made to boil without heating.
Reason (R): Boiling point of water is lowered by decreasing pressure.
Boiling occurs when vapor pressure equals external pressure. Reducing external pressure lowers the boiling point of water. Thus, water can be made to boil at room temperature or even lower without external heating. Both (A) and (R) are true, and (R) correctly explains (A).