Thermodynamics

Question

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A lead bullet penetrates into a solid object and melts. Assuming that 50% of its kinetic energy was used to heat it, the initial speed of the bullet is (the initial temperature of the bullet is 25^oC and its melting point is 300°C). Latent heat of fusion of lead= 2.5 x 10⁴ J/kg and specific heat capacity of lead= 125 J/kg-K

100 m/s

≈ 490 m/s

520 m/s

360 m/s

Solution

≈ 490 m/s

Given:-

Specific heat S = 125 J/kg - K

θ_i = 25^o C

θ_m = 300^o C

m = 2.5 × 10⁴ J/kg

Then,

Heat energy supplied to lead bullet

Q = 50% of KE

= $\frac{1}{2} (\frac{1}{2} m v^{2})$

Q = $\frac{1}{4} {mv}^{2}$

Heat energy utilised for rise of temp and melting of lead bullet

Q' = mc Δθ+ mL

= m ( c Δθ + L )

By equating Q and Q'

$\frac{1}{4} {mv}^{2} = m (c ∆ θ + L)$

⇒ $\frac{v^{2}}{4} = 125 (300 - 25) + 2.5 \times 10^{4}$

⇒ $\frac{v^{2}}{4}$ = 59375 × 4

⇒ v² = $\sqrt{237500}$

⇒ v = 487.5 m/s

⇒ v = 490 m/s

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Thermodynamics

Some More Questions From Thermodynamics Chapter

When a system is taken from state i to state f along the path iaf, it is found that Q = 50 cal and W = 20 cal. Along the path’ ibf Q = 36 cal. W along the path ibf is

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Thermodynamic processes are indicated in the following diagram.

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Column-1 Column-2
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Loaction

Column-1	Column-2
P. Process I	a. Adiabatic
Q. Process II	b. Isobaric
R. Process III	c. Isochoric
S. Process IV	d. Isothermal

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Thermodynamics

Some More Questions From Thermodynamics Chapter

When a system is taken from state i to state f along the path iaf, it is found that Q = 50 cal and W = 20 cal. Along the path’ ibf Q = 36 cal. W along the path ibf is

The work of 146 kJ is performed in order to compress one kilo mole of gas adiabatically and in this process the temperature of the gas increases by 7° C. The gas is(R = 8.3 J mol−1 K−1 )

Which of the following is incorrect regarding the first law of thermodynamics?

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Thermodynamic processes are indicated in the following diagram.Match the following Column-1 Column-2 P. Process I a. Adiabatic Q. Process II b. Isobaric R. Process III c. Isochoric S. Process IV d. Isothermal

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

The work of 146 kJ is performed in order to compress one kilo mole of gas adiabatically and in this process the temperature of the gas increases by 7° C. The gas is

(R = 8.3 J mol⁻¹ K⁻¹ )

A system goes from A to B via two processes I and II as shown in the figure. If ∆U₁ and ∆U₂ are the changes in internal energies in the processes I and II respectively, the

Thermodynamic processes are indicated in the following diagram.

Match the following

Column-1 Column-2
P. Process I a. Adiabatic
Q. Process II b. Isobaric
R. Process III c. Isochoric
S. Process IV d. Isothermal