We shall not delve extensively into polynomial congruence\'s; however, the subje

Question

We shall not delve extensively into polynomial congruence's; however, the subject contains an important theorem of Lagrange that we shall need when we study primitive roots. If f(x) is a polynomial of degree n with integral coefficients (that is, if fix) = a_0x^n + a_1x^n - 1 + ... + a_n), and if p is a prime such that p + a_0, then the congruence f(x) equivalence 0(mod p) has at most n mutually incongruent solutions modulo p. We proceed by mathematical induction on the degree n. If n = 0, then f(x) = a_0. Since a_0 not equal to 0 (mod p), there are no solutions. If n = 1, then f(x) = a_0x + a_1; and we know by Theorem 5-1 that the congruence a_0x equivalence -a_1 (mod p) has exactly one solution (mod p), because g.c.d.(a_0, p) = 1

Explanation / Answer

Mass of water= 1kg= 1000gms

Specific heat of water= 4.184 j/g.deg.c

Temperature rise of water= 32.3-20= 12.3 deg.c

Heat energy change= mass*specific heat* temperature difference=

Change in heat energy of water= 1000*4.184*12.3=51463.2 joules

Let Cp =specific heat of metal mass of metal -52 gm

Temperature difference= 330-32.3=297.7 deg.c

Heat lost = 52*cp*267.7

For adiabatic system, heat lost= heat gained= 51463.2= 52*Cp*297.7

Cp= 51463.2/(52*297.7)=3.32 j/g.deg.c ( b is the correct answer)

2. Molecular weight of Methane = 16 gm

16 gm of methane gives 890 Kj

1.7 gm gives 890*1.7/16=94.5625 Kj

this much heat is gernerated. Hence enthalpy change= -94.56 Kj ( A is the correct answer)

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