The melting temperature of a certain mass of a solid object is $$20$$°C. When a heat Q is added to the object, its $$34material$$ melts. When an additional amount of Q heat is added the material transforms to its liquid state at $$50$$°C. Find the ratio of specific latent heat of fusion (in$$ $$J/g) to the specific heat capacity of the liquid (in$$ J $$g-1$$ °$$C-1) for the material.

Question

The melting temperature of a certain mass of a solid object is $$20$$°C. When a heat Q is added to the object, its $$34material$$ melts. When an additional amount of Q heat is added the material transforms to its liquid state at $$50$$°C. Find the ratio of specific latent heat of fusion (in$$ $$J/g) to the specific heat capacity of the liquid (in$$ J $$g-1$$ °$$C-1) for the material.

Infinity Learn · Accepted Answer

Let the mass of the solid object be m, and specific latent heat of fusion be L ,

According to problem, $Q = \frac{3}{4} mL$ ……..(i)

$2 Q = mL + ms (50 - 20)$ ………(ii)

From (i) and (ii), $\frac{3}{2} mL = mL + 30 ms$

$\Rightarrow \frac{L}{2} = 30 s \Rightarrow \frac{L}{s} = 60$

Calorimetry

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Let the mass of the solid object be m, and specific latent heat of fusion be L ,
According to problem, $Q = \frac{3}{4} mL$ ……..(i)
$2 Q = mL + ms (50 - 20)$ ………(ii)
From (i) and (ii), $\frac{3}{2} mL = mL + 30 ms$
$\Rightarrow \frac{L}{2} = 30 s \Rightarrow \frac{L}{s} = 60$

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Calorimetry

Unlock the full solution & master the concept.

Let the mass of the solid object be m, and specific latent heat of fusion be L ,According to problem, Q=34mL ……..(i)2Q=mL+ms(50−20) ………(ii)From (i) and (ii), 32mL=mL+30ms⇒L2=30s⇒Ls=60

Ready to Test Your Skills?

free study material

Let the mass of the solid object be m, and specific latent heat of fusion be L ,
According to problem, $Q = \frac{3}{4} mL$ ……..(i)
$2 Q = mL + ms (50 - 20)$ ………(ii)
From (i) and (ii), $\frac{3}{2} mL = mL + 30 ms$
$\Rightarrow \frac{L}{2} = 30 s \Rightarrow \frac{L}{s} = 60$