In the relation P= alpha/beta e ^ -alphax /nr theta, P is power, x is distance, n is number - Physics - Units And Measurements

Question

In the relation P= alpha/beta e ^ -alphax /nr theta, P is power,
x is distance, n is number of moles, r is gas constant and theta is
temperature, dimensional formula of beta is____________

Ashish Jain · Accepted Answer

P = αβe-αxnrθ 
where P = power=[ ML2T-3]
x = distance =[L] n = mol = Mol
r = gas constant =[ML2T-2 Mol-1 K-1]
taking log on both side
log p =αβ-αxnrθ
β=-α2xnrβθ log P=LMol [ML2T-2 Mol-1 K-1][K][ ML2T-3]=LM2L4T-5=[M-2L-3T5]P = αβe-αxnrθ 
where P = power=[ ML2T-3]
x = distance =[L] n = mol = Mol
r = gas constant =[ML2T-2 Mol-1 K-1]
taking log on both side
log p =αβ-αxnrθ
β=-α2xnrβθ log P=LMol [ML2T-2 Mol-1 K-1][K][ ML2T-3]=LM2L4T-5=[M-2L-3T5]

In the relation P= alpha/beta. e ^ -alphax /nr theta, P is power, x is distance, n is number of moles, r is gas constant and theta is temperature, dimensional formula of beta is____________