Examine the following plots and predict whether in (i) `P_(1) lt P_(2) "and" T_(1) gt T_(2)` , in (ii) `T_(1) = T_(2)ltT_(3)`, in (iii) `V_(1) gt V_(2), "in" (iv) P_(1) gt P_(2) "or" P_(2) gt P_(1)`

For an ideal gas, an illustration of the different paths, A (B + C) and (D + E) from an intial state P_(1), V_(1), T_(1) to a final state P_(2), V_(2), T_(1) as shown in the given figure. Path (A) represents a reversible isothernal expanison from P_(1)V_(1) to P_(2)V_(2) . Path (B + C) represents a reversible adiabatic expansion (B) from P_(1), V_(1), T_(1) to P_(3), V_(2), T_(2) followed by reversible heating the gas at constant volume (C) from P_(3), V_(2), T_(2) to P_(2), V_(2) T_(1) to P_(1) , V_(2), T_(3) followed by reversible cooling at a constant volume V_(2) (E) from P_(1), V_(2), T_(3) to P_(2), V_(2), T_(1) What is Delta S for path (D + E) ?

State whether (p_1 gt p_2 or p_2 gt p_1) for given mass of a gas ? .

The critical temperature and the critical pressure of a gas are T_(c) and P_(c) , respectively. If the gas exists at a temperature of T and a pressure P, then under which of the following conditions will the gas not be liquefied? (i) T gt T_(c) , P gt P_(c) (ii) T=T_(c),PgtP_(c) (iii) T=T_(c),PltP_(c) (iv) T lt T_(c),P=P_(c)

For 1 mol of an ideal gas, V_(1)gtV_(2)gtV_(3) in fig. ( I ), T_(1)gtT_(2)gtT_(3) in fig. ( II ), P_(1)gtP_(2)gtP_(3) in fig. ( III ), and T_(1)gtT_(2)gtT_(3) in fig. ( IV ) , then which curves are correct.

For 1 mol of an ideal gas, V_(1)gtV_(2)gtV_(3) in fig. ( I ), T_(1)gtT_(2)gtT_(3) in fig. ( II ), P_(1)gtP_(2)gtP_(3) in fig. ( III ), and T_(1)gtT_(2)gtT_(3) in fig. ( IV ) , then which curves are correct.

Find p (0) p, (1) and p (2) for each of the following polynomials. (i) p (x) = x ^(2) - x +1 (ii) p (z) =z ^(3) (iii) p (y)=2 + y +2y ^(2) - y ^(3) (iii) p (z) =z ^(3) (iv) p (t) = (t-1) (t +1) (v) p (x) = x ^(2) - 3x +2