In an energy recycling process, X g of steam at 100 °C becomes water at 100 °C which converts Y g of ice at 0 °C into water at 100 °C. The ratio of X and Y will be
A ratio is a mathematical comparison of two quantities showing how many times one value contains or is contained in another. It is expressed in the form “a:b” or as a fraction. Ratios help compare sizes, quantities or relationships and are widely used in math, science and daily life applications.
Class 11 Physics Chapter 10 Thermal Properties of Matter explains heat, temperature and their effects on matter. It covers thermal expansion of solids, liquids and gases, specific heat capacity, calorimetry, heat transfer methods like conduction, convection and radiation. These concepts are essential for CBSE Exam 2024-25 preparation and practical understanding in science and engineering fields.
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Let’s analyze the energy transfer to solve this problem.
Step 1: Energy released by X g of steam
When steam at 100°C condenses to water at 100°C, the energy released is:
Qₛₜₑₐₘ = X ⋅ Lᵥ
where Lᵥ = 540 cal/g (latent heat of vaporization of water).
Step 2: Energy absorbed by Y g of ice
The ice first melts into water at 0°C, and then this water is heated to 100°C. The total energy absorbed by Y g of ice is:
Qᵢcₑ = Y ⋅ Lf + Y ⋅ c ⋅ ΔT
where:
– Lf = 80 cal/g (latent heat of fusion of ice),
– c = 1 cal/g°C (specific heat capacity of water),
– ΔT = 100°C.
Put values:
Qᵢcₑ = Y ⋅ 80 + Y ⋅ 1 ⋅ 100 = Y ⋅ (80 + 100) = Y ⋅ 180 cal.
Step 3: Energy conservation
The energy released by steam is equal to the energy absorbed by ice:
X ⋅ 540 = Y ⋅ 180
Step 4: Solve for X/Y
X / Y = 180 / 540 = 1 / 3
Final Answer:
The ratio of X and Y is 1:3.
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