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Chapter 1: Problem 131

Dimensional formula of latent heat is ........ (a) \(\mathrm{M}^{0} \mathrm{~L}^{2} \mathrm{~T}^{-2}\) (b) \(\mathrm{M}^{2} \mathrm{~L}^{0} \mathrm{~T}^{-2}\) (c) \(\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-1}\) (d) \(\mathrm{M}^{2} \mathrm{~L}^{2} \mathrm{~T}^{-1}\)

Short Answer

Expert verified
The dimensional formula of latent heat is \(\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-2}\).

Step by step solution

01

Identify known dimensional formulas

The given equation for Latent heat (L) has three variables: 1. mass (m) 2. specific heat (c) 3. temperature change (ΔT) The dimensional formula of mass is M. The dimensional formula of temperature change is K. We need to find the dimensional formula for specific heat.
02

Find dimensional formula of specific heat

The specific heat can be determined using the following formula: specific heat (c) = energy / (mass × temperature change) We know that: Energy (E) has the dimensions of mass (M), length (L), and time (T): \([E] = M^1 L^2 T^{-2}\) Temperature change (ΔT) has the dimensions of Kelvin (K): \([ΔT] = K^1\) Now, we can solve for the dimensional formula of specific heat (c): \([c] = \frac{[E]}{[m][ΔT]}\)
03

Calculate the dimensional formula of specific heat

To calculate the dimensional formula of specific heat (c), substitute the known dimensional formulas for energy, mass, and temperature change: \([c] = \frac{M^1 L^2 T^{-2}}{M^1 K^1}\) Now, simplify the expression: \([c] = L^2 T^{-2} K^{-1}\)
04

Determine the dimensional formula of latent heat

Now that we have the dimensional formula for specific heat, we will find the dimensional formula of latent heat (L) by using the equation: Latent heat (L) = (mass × specific heat × temperature change) In terms of dimensional formulas, we have: \([L] = [m][c][ΔT]\) Substitute the known dimensional formulas for mass, specific heat, and temperature change: \([L] = M^1 \cdot (L^2 T^{-2} K^{-1}) \cdot K^1\) Now, simplify the expression: \([L] = M^1 L^2 T^{-2}\) Therefore, the dimensional formula of latent heat is \(\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-2}\), which matches option (c).

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Most popular questions from this chapter

Which of the following numerical value have significant figure \(4 ?\) (a) \(1.011\) (b) \(0.010\) (c) \(0.001\) (d) \(0.100\)

Dimensional formula for capacitance (C) (a) \(\mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^{4} \mathrm{~A}^{2}\) (b) \(\mathrm{M}^{1} \mathrm{~L}^{-2} \mathrm{~T}^{4} \mathrm{~A}^{2}\) (c) \(\mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^{3} \mathrm{~A}^{1}\) (d) \(\mathrm{M}^{3} \mathrm{~L}^{1} \mathrm{~T}^{-1} \mathrm{~A}^{-2}\)

Equation of \(\ell_{1}=\ell_{0}\left[1+\alpha\left(\mathrm{T}_{2}-\mathrm{T}_{1}\right)\right]\) find out the dimensions of the coefficient of linear expansion \(\alpha\) suffix. (a) \(\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{1} \mathrm{~K}^{1}\) (b) \(\mathrm{M}^{0} \mathrm{~L}^{1} \mathrm{~T}^{1} \mathrm{~K}^{1}\) (c) \(\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{0} \mathrm{~K}^{1}\) (d) \(\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{0} \mathrm{~K}^{-1}\)

Write the dimensional formula of the ratio of linear momentum to angular momentum. (a) \(\mathrm{M}^{0} \mathrm{~L}^{-1} \mathrm{~T}^{0}\) (b) \(\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{0}\) (c) \(\mathrm{M}^{0} \mathrm{~L}^{1} \mathrm{~T}^{0}\) (d) \(\mathrm{M}^{0} \mathrm{~L}^{1} \mathrm{~T}^{1}\)

Test if the following equation are dimensionally correct \((\mathrm{S}=\) surface tension \(\rho=\) density \(\mathrm{P}=\) pressure \(\mathrm{v}=\) volume \(\mathrm{n}=\) coefficient of viscosity \(\mathrm{r}=\) radius \()\) (a) \(\mathrm{h}=[(2 \mathrm{~S} \cos \theta) /(\rho \mathrm{rg})]\) (b) \(\mathrm{v}=\sqrt{(p / \rho)}\) (c) $\mathrm{v}=\left[\left(\pi \mathrm{pr}^{4} \mathrm{t}\right) /(8 \mathrm{n} \ell)\right]$ (d) all correct
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