Question

The mass of a hypothetical substance that melts at 5°C is mx = 5.5 kg and its temperature is Tx = 5°C. This substance, as a solid, is added to mw = 19.5 kg of water at Ti = 65.0°C. The final temperature of the mixture became Tf = 260C.

Calculate the latent heat of fusion of this substance. Express your answer with one decimal place in units shown.

Useful data:
Assume that the specific heats are: cx = 0.980 kJ/kg°C and cwater = 4.186 kJ/kg°C.

Answer 1

Answer:

Latent heat of fusion for the unknown liquid is given as

$L = 558.23 kJ/kg$

Explanation:

As we know that substance is melt due to thermal energy given by the water

As per energy conservation thermal energy given by the water is equal to the energy absorbed by the unknown liquid

So here we know that heat required to melt down the unknown liquid is given as

$Q = m_x L + m_xc_x(\Delta T')$

now heat given by water to change its temperature

$Q = m_w s(\Delta T)$

now we have

$m_x L + m_xc_x\Delta T' = m_w s(\Delta T)$

$5.5(L) + 5.5(0.980)(26 - 5) = 19.5(4.186)(65 - 26)$

$5.5 L + 113.19 = 3183.453$

$5.5 L = 3070.26$

$L = 558.23 kJ/kg$

#Learn

Topic : Mixing of two liquids

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