An ideal gas (molar specific heat $C_{V} = \frac{5 R}{2}$ ) is taken along paths acb, adb and ab. $P_{2} = 2 P_{1}, V_{2} = 2 V_{1}$ . Along ab, P = kV where k is a constant. The various parameters are shown in figure. Match the column I with the corresponding option of column II.

Column I Column II

i. $W_{a c b}$ p $\frac{15 R T_{1}}{2}$

ii. $W_{a d b}$ q $\frac{- 15 R T_{1}}{2}$

iii. $U_{a b}$ r $R T_{1}$

iv. $U_{b c a}$ s $2 R T_{1}$

Now match the given columns and select the correct option from the codes given below.

i - r, ii - s, iii - p, iv - q

No worries! We‘ve got your back. Try BYJU‘S free classes today!

i - s, ii - r, iii - p, iv - q

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

i - r, ii - s, iii - q, iv - p

No worries! We‘ve got your back. Try BYJU‘S free classes today!

i - s, ii - r, iii - q, iv - p

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B i - s, ii - r, iii - p, iv - q
$W_{a c b} = W_{a c} + W_{c b} = 0 + P_{2} (V_{2} - V_{1}) = P_{2} V_{1} = 2 P_{1} V_{1} = 2 R T_{1} (∵ V_{2} = 2 V_{1}) W_{a d b} = W_{a d} + W_{d b} = P_{1} (V_{2} - V_{1}) + 0 = P_{1} V_{1} = R T_{1} U_{a b} = U_{a c} + U_{c b} = (Q_{a c} - W_{a c}) + (Q_{c b} - W_{c b}) = C_{V} (T_{c} - T_{1}) + C_{V} (T_{2} - T_{C}) = C_{V} (T_{2} - T_{1}) = \frac{5 R}{2} (T_{2} - T_{1}) (G i v e n C_{V} = \frac{5 R}{2}) F o r a n i d e a l g a s, \frac{P_{1} V_{1}}{T_{1}} = \frac{P_{2} V_{2}}{T_{2}} P_{2} = 2 P_{1} a n d V_{2} = 2 V_{1} \Rightarrow T_{2} = 4 T 1 ∴ U_{a b} = \frac{5 R}{2} (T_{2} - T_{1}) = \frac{15 R T_{1}}{2} F o r t h e e n t i r e c y c l e, Δ U = 0 \Rightarrow U_{b c a} = - U_{a b} U_{b c a} = \frac{- 15 R T_{1}}{2}$

Suggest Corrections

Similar questions

C_{V} = \frac{5 R}{2}

P_{2} = 2 P_{1}, V_{2} = 2 V_{1}

\begin{matrix} Column-I & Column-II p. Pancreas & i. FSH and LH q. Anterior pituitary & ii. Estrogen r. Testes & iii. Glucagon s. Ovary & iv. Androgens \end{matrix}

I

II

\begin{matrix} Column - I & Column - II i.Velocity of a particle following & (p) α equation x = u (t - 8) + α (t - 2)^{2} at t = 0 ii.Acceleration of a particle moving according to equation & (q) 2 α x = u (t - 8) + α (t - 2)^{2} at t = 0 iii.Velocity of the particle moving & (r) u according to equation x = u t + 5 α t^{2} ln (1 + \frac{t}{2}) + α t^{2} at t = 0 iv.Acceleration of the particle moving & (s) u - 4 α according to the equation x = u t + 5 α t^{2} (1 + \frac{t}{2}) + α t^{2} at t = 0 \end{matrix}

\begin{matrix} Column-X & Column-Y (p) Vapour density & (i) Unitless (q) Mole & (ii) 1 mol of electrons (r) 12 g Carbon & (iii) Collection of 6.023 \times 10^{23} atoms (s) 96500 C & (iv) Molecular mass (Numerical value) \times \frac{1}{2} \end{matrix}

\begin{matrix} Column I & Column II i . & O S F_{2} & p . & Tetrahedral i i . & O_{2} S F_{2} & q . & Linear i i i . & X e F_{4} & r . & Square planar i v . & C l O_{4}^{-} & s . & Trigonal pyramidal v . & I_{3}^{-} & t . & See - saw \end{matrix}

Join BYJU'S Learning Program