80g of water at 30° C are poured on a large block of ice at 0°C. The mass of ice that melts is
Mass is a fundamental property of matter that measures the amount of substance in an object. It is a scalar quantity and remains constant regardless of location. Mass is typically measured in kilograms (kg) and determines an object’s resistance to acceleration when a force is applied (inertia).
In Chapter 10 of Class 11 Physics Thermal Properties of Matter the relationship between temperature and heat transfer is discussed. Heat is transferred through conduction convection and radiation. The chapter also covers the concepts of specific heat latent heat and thermal expansion. The study of black bodies and their radiation is included.
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To solve this problem, we need to use the principle of conservation of energy. The heat lost by the warm water will be used to melt the ice.
The formula to calculate the heat required to melt the ice is:
Q = m ⋅ Lբ
Where:
– Q is the heat lost by the water (in calories),
– m is the mass of the ice melted,
– Lբ is the latent heat of fusion of ice (which is 80 cal/g).
The heat gained by the ice is:
Q = m_w ⋅ c_w ⋅ ΔT
Where:
– mᵥᵥ is the mass of water,
– cᵥᵥ is the specific heat capacity of water (which is 1 cal/g°C),
– ΔT is the temperature change of the water (in this case, from 30°C to 0°C, so ΔT = 30°C).
Now, we can calculate the heat gained by the ice:
Q = 80 g ⋅ 1 cal/g°C ⋅ 30°C = 2400 cal
Now, we can find the mass of the ice that melts using the equation for heat required to melt the ice:
2400 cal = m ⋅ 80 cal/g
m = 2400 / 80 = 30 g
Thus, the mass of ice that melts is 30 g.