An unknown mass of a certain solid, initially at 60⁰C, is heated at a uniform at a uniform rate. After 4.0 min the solid reaches its melting point of 80⁰C, and it remains at that temperature for 3.0 min until completely melted. After a further 6.0 min of heating, the resulting liquid is at 100⁰C. If the specific heat capacity of the substance in the solid state is 2.0 kJ/kg ⁰C, find the heat of fusion of the substance and its specific heat capacity in the liquid state.
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walang sagot
54 kJ / kg - °c
c= 3.6
To find the heat of fusion of the substance and its specific heat capacity in the liquid state, we need to use the formula for heat transfer:
Q = mcΔT
Where Q is the heat transferred, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.
Let's break down the given information and calculate the values step by step:
1. In the first phase, the solid is heated from 60⁰C to 80⁰C. We know that the specific heat capacity of the substance in the solid state is 2.0 kJ/kg ⁰C. We need to find the heat transferred during this phase.
ΔT1 = 80⁰C - 60⁰C = 20⁰C
The heat transferred during this phase is given by:
Q1 = mcΔT1
Since the mass of the substance is unknown, we'll use the symbol 'm' to represent it.
Q1 = 2.0 kJ/kg ⁰C * m * 20⁰C
2. In the second phase, the solid melts into a liquid at a constant temperature of 80⁰C for 3 minutes. During this phase, the temperature doesn't change, so there is no heat transfer involved.
Q2 = 0 kJ
3. In the third phase, the liquid is further heated from 80⁰C to 100⁰C. We need to find the heat transferred during this phase.
ΔT3 = 100⁰C - 80⁰C = 20⁰C
Since the substance is now in the liquid state, we need to find its specific heat capacity in this state, denoted by 'cL.'
Q3 = mcLΔT3
Now, we can add up the total heat transferred during these three phases:
Total heat transferred = Q1 + Q2 + Q3
Since the total time is 4 minutes + 3 minutes + 6 minutes = 13 minutes, we can assume that the rate of heating is constant.
Total heat transferred = (2.0 kJ/kg ⁰C * m * 20⁰C) + 0 kJ + (cL * m * 20⁰C)
Now, let's equate the total heat transferred with the time taken:
Total heat transferred = (rate of heating * time taken)
Total heat transferred = (Q1 + Q2 + Q3) = (rate of heating * 13 minutes)
Solving this equation will give us the values for the heat of fusion (Q2) and the specific heat capacity in the liquid state (cL). However, since the mass (m) of the substance is unknown, we won't be able to find the specific values without further information.